Provided are a signal processing apparatus and a method thereof that can convert amplitude sampling data outputted from an analog/digital converter into phase data and converts the phase data into amplitude data at high speed. The signal processing apparatus includes: an A/D (analog to digital) converter converting an inphase frequency signal and a quadrature frequency signal into amplitude sampling data including digital inphase data and digital quadrature data; a phase shifter including a phase shift lookup table that converts all amplitude sampling data outputtable from the A/D converter into phase values and approximates the phase values into first approximate integers, and thereafter, converts the first approximate integers into phase data of predetermined bits and stores the phase data, and converting the amplitude sampling data inputted from the A/D converter into the phase data by referring to the phase shift lookup table; a phase data memory storing the phase data outputted from the phase shifter; an amplitude converter including an amplitude conversion lookup table that converts all phase data outputtable from the phase shifter into amplitude values and approximates the amplitude values into second approximate integers, and converts the second approximate integers into amplitude data including digital inphase data and digital quadrature data and stores the amplitude data, and converting the phase data stored in the phase data memory into amplitude data by referring to the amplitude conversion lookup table; and a D/A converter converting the amplitude data outputted from the amplitude converter into an inphase frequency signal and a quadrature frequency signal.